.TH std::comp_ellint_3,std::comp_ellint_3f,std::comp_ellint_3l 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::comp_ellint_3,std::comp_ellint_3f,std::comp_ellint_3l \- std::comp_ellint_3,std::comp_ellint_3f,std::comp_ellint_3l

.SH Synopsis
   double      comp_ellint_3( double k, double nu );

   float       comp_ellint_3( float k, float nu );
   long double comp_ellint_3( long double k, long double nu );   \fB(1)\fP
   float       comp_ellint_3f( float k, float nu );

   long double comp_ellint_3l( long double k, long double nu );
   double      comp_ellint_3( IntegralType k, IntegralType nu ); \fB(2)\fP

   1) Computes the complete elliptic integral of the third kind of arg.
   2) A set of overloads or a function template accepting an argument of any integral
   type. Equivalent to \fB(1)\fP after casting the argument to double.

   As all special functions, comp_ellint_3 is only guaranteed to be available in
   <cmath> if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at
   least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before
   including any standard library headers.

.SH Parameters

   nu - value of a floating-point or integral type
   k  - value of a floating-point or integral type

.SH Return value

   If no errors occur, value of the complete elliptic integral of the second kind of
   arg, that is ellint_3(k, nu, π/2), is returned.

.SH Error handling

   Errors may be reported as specified in math_errhandling.

     * If the argument is NaN, NaN is returned and domain error is not reported.
     * If either |k| > 1 or |nu| > 1, a domain error may occur.

.SH Notes

   Implementations that do not support TR 29124 but support TR 19768, provide this
   function in the header tr1/cmath and namespace std::tr1.

   An implementation of this function is also available in boost.math.

.SH Example

   (works as shown with gcc 6.0)


// Run this code

 #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
 #include <cmath>
 #include <iostream>

 int main()
 {
     double hpi = std::acos(-1) / 2;
     std::cout << "Π(0, 0.75) = " << std::comp_ellint_3(0, 0.75) << '\\n'
               << "π/2 = " << hpi << '\\n'
               << "Π(0.5, 0.75) = " << std::comp_ellint_3(0.5, 0.75) << '\\n'
               << "Π(0.5, 0.75, π/2) = " << std::ellint_3(0.5, 0.75, hpi) << '\\n';
 }

.SH Output:

 Π(0, 0.75) = 3.14159
 π/2 = 1.5708
 Π(0.5, 0.75) = 3.45372
 Π(0.5, 0.75, π/2) = 3.45372

.SH External links

   Weisstein, Eric W. "Complete Elliptic Integral of the Third Kind." From MathWorld--A
   Wolfram Web Resource.

.SH See also

   ellint_3  (incomplete) elliptic integral of the third kind
   ellint_3f \fI(function)\fP
   ellint_3l
